1. Field of the Invention
The present invention relates to systems and methods for guiding spacecraft, and in particular to a system and method for guiding a spacecraft to a soft landing on a planetary surface.
2. Description of the Related Art
To increase the science return of future missions to Mars, and to enable sample return missions, the accuracy with which a lander can be delivered to the Martian surface must be improved by orders of magnitude over the current capabilities. Towards this goal, our prior work developed a convex optimization based minimum-fuel powered descent guidance algorithm. Here, we extend this approach to handle the case when no feasible trajectory to the target exists. In this case, our objective is to generate the minimum landing error trajectory, which is the trajectory that minimizes the distance to the prescribed target while utilizing the available fuel optimally. This problem is inherently a non-convex optimal control problem due to a nonzero lower bound on the magnitude of the feasible thrust vector. We first prove that an optimal solution of a convex relaxation of the optimal control problem is also optimal for the original non-convex problem, which we refer to as the lossless convexification of the original non-convex problem. Then we show that the minimum landing error trajectory generation problem can be posed as a convex optimization problem, in particular as a Second-Order Cone Program, and solved to global optimality with deterministic convergence. This makes the approach amenable to onboard implementation for real-time applications.